## New approach to pulse propagation in nonlinear dispersive optical media |

JOSA B, Vol. 29, Issue 10, pp. 2958-2963 (2012)

http://dx.doi.org/10.1364/JOSAB.29.002958

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### Abstract

We develop an intuitive approach for studying propagation of optical pulses through nonlinear dispersive media. Our new approach is based on the impulse response of linear systems, but we extend the impulse response function using a self-consistent time-transformation approach so that it can be applied to nonlinear media as well. Numerical calculations based on our new approach show excellent agreement with the generalized nonlinear Schrödinger equation in the specific case of the Kerr nonlinearity in both the normal and anomalous dispersion regimes. An important feature of our approach is that it works directly with the electric field associated with an optical pulse and can be applied to pulses of arbitrary width. Numerical calculations performed using single-cycle optical pulses show that our results agree with those obtained with the finite-difference time-domain technique using considerably more computing resources.

© 2012 Optical Society of America

## 1. INTRODUCTION

2. P. Agostini and L. F. DiMauro, “The physics of attosecond light pulses,” Rep. Prog. Phys. **67**, 813–855 (2004). [CrossRef]

4. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. **78**, 3282–3285 (1997). [CrossRef]

5. G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics **5**, 656–664 (2011). [CrossRef]

6. G. D. Tsakiris, K. Eidmann, J. M. Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys. **8**, 19 (2006). [CrossRef]

7. A. Kumar, “Ultrashort pulse propagation in a cubic medium including the Raman effect,” Phys. Rev. A **81**, 013807 (2010). [CrossRef]

9. S. Nakamura, N. Takasawa, and Y. Koyamada, “Comparison between finite-difference time-domain calculation with all parameters of Sellmeier’s fitting equation and experimental results for slightly chirped 12 fs laser pulse propagation in a silica fiber,” J. Lightwave Technol. **23**, 855–863 (2005). [CrossRef]

## 2. PULSE PROPAGATION IN A LINEAR DISPERSIVE MEDIUM

10. Y. Xiao, G. P. Agrawal, and D. N. Maywar, “Spectral and temporal changes of optical pulses propagating through time-varying linear media,” Opt. Lett. **36**, 505–507 (2011). [CrossRef]

11. Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Nonlinear pulse propagation: A time-transformation approach,” Opt. Lett. **37**, 1271–1273 (2012). [CrossRef]

## 3. EXTENSION TO A NONLINEAR DISPERSIVE MEDIUM

11. Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Nonlinear pulse propagation: A time-transformation approach,” Opt. Lett. **37**, 1271–1273 (2012). [CrossRef]

11. Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Nonlinear pulse propagation: A time-transformation approach,” Opt. Lett. **37**, 1271–1273 (2012). [CrossRef]

## 4. PULSES CONTAINING MANY OPTICAL CYCLES

## 5. PULSES CONTAINING A FEW OPTICAL CYCLES

4. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. **78**, 3282–3285 (1997). [CrossRef]

## 6. CONCLUDING REMARKS

10. Y. Xiao, G. P. Agrawal, and D. N. Maywar, “Spectral and temporal changes of optical pulses propagating through time-varying linear media,” Opt. Lett. **36**, 505–507 (2011). [CrossRef]

## ACKNOWLEDGMENTS

## REFERENCES

1. | G. P. Agrawal, |

2. | P. Agostini and L. F. DiMauro, “The physics of attosecond light pulses,” Rep. Prog. Phys. |

3. | G. P. Agrawal, |

4. | T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. |

5. | G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics |

6. | G. D. Tsakiris, K. Eidmann, J. M. Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys. |

7. | A. Kumar, “Ultrashort pulse propagation in a cubic medium including the Raman effect,” Phys. Rev. A |

8. | C. V. Hile and W. L. Kath, “Numerical solutions of Maxwell’s equations for nonlinear-optical pulse propagation,” J. Opt. Soc. Am. B |

9. | S. Nakamura, N. Takasawa, and Y. Koyamada, “Comparison between finite-difference time-domain calculation with all parameters of Sellmeier’s fitting equation and experimental results for slightly chirped 12 fs laser pulse propagation in a silica fiber,” J. Lightwave Technol. |

10. | Y. Xiao, G. P. Agrawal, and D. N. Maywar, “Spectral and temporal changes of optical pulses propagating through time-varying linear media,” Opt. Lett. |

11. | Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Nonlinear pulse propagation: A time-transformation approach,” Opt. Lett. |

12. | K. E. Oughstun and G. C. Sherman, |

**OCIS Codes**

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: July 30, 2012

Revised Manuscript: August 28, 2012

Manuscript Accepted: September 1, 2012

Published: September 28, 2012

**Virtual Issues**

October 10, 2012 *Spotlight on Optics*

**Citation**

Yuzhe Xiao, Drew N. Maywar, and Govind P. Agrawal, "New approach to pulse propagation in nonlinear dispersive optical media," J. Opt. Soc. Am. B **29**, 2958-2963 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-10-2958

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### References

- G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).
- P. Agostini and L. F. DiMauro, “The physics of attosecond light pulses,” Rep. Prog. Phys. 67, 813–855 (2004). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).
- T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997). [CrossRef]
- G. Sansone, L. Poletto, and M. Nisoli, “High-energy attosecond light sources,” Nat. Photonics 5, 656–664 (2011). [CrossRef]
- G. D. Tsakiris, K. Eidmann, J. M. Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys. 8, 19 (2006). [CrossRef]
- A. Kumar, “Ultrashort pulse propagation in a cubic medium including the Raman effect,” Phys. Rev. A 81, 013807 (2010). [CrossRef]
- C. V. Hile and W. L. Kath, “Numerical solutions of Maxwell’s equations for nonlinear-optical pulse propagation,” J. Opt. Soc. Am. B 13, 1135–1146 (1996). [CrossRef]
- S. Nakamura, N. Takasawa, and Y. Koyamada, “Comparison between finite-difference time-domain calculation with all parameters of Sellmeier’s fitting equation and experimental results for slightly chirped 12 fs laser pulse propagation in a silica fiber,” J. Lightwave Technol. 23, 855–863 (2005). [CrossRef]
- Y. Xiao, G. P. Agrawal, and D. N. Maywar, “Spectral and temporal changes of optical pulses propagating through time-varying linear media,” Opt. Lett. 36, 505–507 (2011). [CrossRef]
- Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Nonlinear pulse propagation: A time-transformation approach,” Opt. Lett. 37, 1271–1273 (2012). [CrossRef]
- K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer, 1994).

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